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Simplify and find the value:

{sin}^(4) a - {cos}^(4) a - 2 {sin}^(2) a


User Valdis
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1 Answer

6 votes

Answer:

-1

Explanation:

Trigonometry identity: sin²a + cos²a = 1 cos²a = 1 - sin²a

sin⁴a - cos⁴a - 2sin²a

= sin⁴a - (cos²a)² - 2sin²a

= sin⁴a - (1 - sin²a)² - 2sin²a

= sin⁴a - (1 - 2sin²a + sin⁴a) - 2sin²a

= sin⁴a - 1 + 2sin²a - sin⁴a - 2sin²a

= -1

User Cwhisperer
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